Chapter 6. Conflict Detection and Resolution
6.3. Free-flight approaches
6.3.3. An example of reactive approach: neural
In 1996, we proposed another approach using neural network (NN) to solve conflicts in the horizontal plane [DUR 96c].
6.3.3.1. Problem modeling
The problem we wanted to solve was the following: an aircraft flying at a constant speed detects another aircraft flying at the same altitude (more or less1;000ft) in a20
NM diameter disk. We want to build an NN that modifies the heading of this aircraft when there is a conflict (respecting operational constraint of45 maximum per15s).
The other aircraft is supposed to have the same embarked system so that it also detects the first aircraft and reacts using the same NN with different inputs.
The system was supposed to use an embarked radar to detect other aircraft.
Consequently, all the inputs of the NN had to be given by the radar information.
In our problem, it seems clear that if no conflict occurs, no NN is needed to solve it. Consequently, at each time step, we first check if both aircraft can reach their destination without heading change and without generating conflicts. In such a case, we do not modify aircraft headings. If we detect a conflict in less than 20 min, we compute a new heading for both aircraft with the NN.
6.3.3.2. The inputs
Seven inputs were used by the NN (see Figure 6.4):
– the heading to the destination and its absolute valuej j(in degrees);
– the distance to the other aircraft and its gradientddt; – the bearing of the other aircraft (in degrees);
– the converging angle of the trajectories ; – a bias set to1.
Destination α
β λ aircaft 1
aircraft 2 γ
Figure 6.4.The neural network inputs of aircraft 1
6.3.3.3. The neural network structure
The NN structure was as simple as possible. We chose a three-layer network (see Figure 6.5), which returned a heading change of45 maximum (for a time step of 15s). We used the following activation function:
act(s) = 1 1 +e s
In Figure 6.5, the first layer takes the six inputs described earlier along with the bias.
The second layer holds13units whereas the third layer holds the output unit.
β γ d /dtλ
λ
|α|
α 1
heading change 1
Figure 6.5.The neural network structure
6.3.3.4. Learning the neural network weights
Classical back-propagation of gradient could not be used in our case because conflict-free trajectories were not known in every configuration. We decided to use unsupervised learning with genetic algorithm and compared results of the network with optimal trajectories computed by the large and nonlinearly constrained extended Lagrangian optimization techniques software named LANCELOT [CON 92].
6.3.3.5. Evolutionary algorithm used
We used classical evolutionary algorithms (EAs) described in the literature [GOL 89, MIC 92]. Each NN was coded by a matrix of real numbers that contained the weights of the NN. “Stochastic remainder without replacement selection” was
used: First, the fitnessfi of thenelements of the population is computed, and the averagea=P
fi=nof all the fitness is computed. Then each element is reproduced ptimes in the new population, with p = truncate(n fi=a). The population is finally completed using probabilities proportional tofi p a=nfor each element.
Arithmetic crossover was used: two parents are recombined by choosing randomly 2[ 0:5;1:5]and creating child1(resp. child2) as the barycenter of some randomly chosen weights of(parent1; )(resp.(parent1;1 )) and(parent2;1 )(resp.
(parent2; )). In the experiments, the crossover probability used was60%.
For the mutation operator, we chose to add a Gaussian noise to one of the weights of the NN. The mutation probability used was15%.
In the experiments, the population size was500and the number of generations was 500.
6.3.3.6. Computing the fitness
One of the main issues was to know how to compute thefitnessof a chromosome.
The constrained problem to solve takes the following criteria into account:
– aircraft trajectories must be conflict free;
– delay due to deviation must be as low as possible.
To compute the fitness, a panel of different conflict configurations was created.
The fitness was computed as follows:
F = 1 De V
whereDis the average delay due to deviations andV is the average number of conflict violations.
6.3.3.7. The learning examples
To learn the weights of the NNs, 12 configurations were created. In each configuration, att= 0aircraft are20NM distant.
In four configurations (see Figure 6.6), aircraft have the same speed and converge with different angles (20 ,60 ,120 ,150 ). In four other configurations, aircraft have different speed, their headings are calculated to generate a conflict (one aircraft speed is500knots (kts) and that of the other aircraft is300,350,400and450kts).
20°
120°
60°
150°
1 2
3
1 2
3
4 4
Figure 6.6.Four configurations at the same speed and four configurations at the different speeds
In two configurations, aircraft have opposite headings and the same speed. In two other configurations, aircraft have the same heading but different speeds (see Figure 6.7).
2 1
1 2
Figure 6.7.Two configurations of facing aircraft and two configurations of parallel aircraft
Because of symmetries, these12configurations summarize all the situations that can happen. We call “positive configuration” (see Figure 6.8) a configuration in which the angle between the slowest and the fastest aircraft is positive. When a “negative configuration” occurs, the symmetrical positive configuration is used in the NN to calculate the deviation. Therefore, some of the inputs and the outputs are given the opposite sign.
6.3.3.8. Numerical results
Figures 6.9–6.13 compare the results obtained with the NN to optimal solution calculated with a gradient method (when the work was done, LANCELOT was one of the most efficient softwares to compute optimal trajectories on this problem, but it was still very slow). Results showed that solutions found with the NN are less optimal,
but the loss of optimality is not significant (the delay induced by the NN was never more than four times the minimal delay, which is generally very small).
fastest aircraft
slowest aircraft
− +
Figure 6.8.Symmetrical configurations
The configurations used to compare the NN to optimal solutions are not learned configurations. This shows the capacity of the NN to generalize to non-learned situations. For each solution, the mean lengthening of the trajectories is given in percentage:
– Figure 6.9 gives an example of conflict at90 in which aircraft have the same speed. NN (1:08%) and optimal solution (0:26%) are similar.
Figure 6.9.Neural network solution (left), optimal solution (right)
– Figure 6.10 gives an example of conflict at15 in which aircraft have the same speed. Such a conflict is particularly difficult to solve. Solutions are different, but for such a difficult conflict, the NN (2:30%) gives a solution that is robust and quite as
good as the optimal solution (2:23%). This conflict is the most difficult conflict to solve (in the five examples presented). It is interesting to see that the difference of lengthenings is the smallest.
Figure 6.10.Neural network solution (left), optimal solution (right)
– Figure 6.11 gives an example of aircraft at different speeds (400 and500 kts) with crossing at a small angle (30 ). The NN solution (1:32%) appears very similar to the optimal solution (0:28%) even if its lengthening is worse.
Figure 6.11.Neural network solution (left), optimal solution (right)
– Figure 6.12 gives an example of aircraft crossing on the same route. This problem is easy to solve and solutions are similar. The NN solution (1:18%) is robust but worse than the optimal solution (0:25%).
Figure 6.12.Neural network solution (down), optimal solution (up)
– Figure 6.13 gives an example of aircraft flying on parallel routes at different speeds. This problem is easy to solve. Solutions are similar. The NN solution (1:02%) is robust but worse than the optimal solution (0:21%).
Figure 6.13.Neural network solution (down), optimal solution (up)
These five examples show that the principal advantage of the NN is to be very robust. It does not give optimal solutions. However, it gives very good solutions for difficult conflicts. Tests conducted on non-learned situations gave as good results as tests conducted on learned situations. It is however hard to extend this research to conflicts involving more than two aircraft: building a learning set of example becomes very challenging.